Physical origin of the non‑monotonic threshold angle at high momentum

Determine the physical mechanism responsible for the observed upturn of the threshold incidence angle θ0 as a function of the initial linear momentum p/M at large p/M in dynamical capture of two equal‑mass non‑spinning black holes, where θ0 denotes the critical angle separating close hyperbolic scattering from capture; establish whether spin‑orbit and spin‑spin interactions induced during the close encounter account for this non‑monotonic behavior.

Background

The paper defines a threshold incidence angle θ0 that separates pure close hyperbolic encounters (scattering) from dynamical capture. Using a two‑emission sin‑Gaussian plus ringdown model fitted to numerical relativity simulations, the authors extract θ0 across several initial momenta p/M and find that θ0 generally decreases with p/M but exhibits an unexpected upturn for the most relativistic configurations.

They suggest a speculative explanation involving enhanced spin‑orbit and spin‑spin couplings due to significant spin induction at high p/M, which could increase the effective attraction and facilitate capture, but emphasize that the effect is not understood and requires dedicated investigation.